We discuss several fundamental questions concerning the problem of minimizing a nonlinear function subject to a set of inequality constraints. We begin by asking: What makes the problem intrinsically difficult to solve, and which characterizations of the solution make its solution more tractable? This leads to a discussion of two important methods of solution: active set and interior points. We make a critical assessment of the two approaches, and describe the main issues that must be resolved to make them effective in the solution of very large problems.